Nikolai E. Terentiev

Superresolution when PSF is indefinite

Situation when Point Spread Function (PSF) of the device is indefinite or it is roughly appreciated takes place almost always. In an optical wave range PSF (optics + atmosphere) is frequently indefinite, because of an indefinite conditions of scattering and turbulence of an atmosphere. The antenna pattern or PSF of radio telescopes cannot be measured. The near zone of the radio telescopes is so big that it does not allow to measure the antenna pattern or PSF by the ground based methods. The methods of evaluation of PSF on details of the images are considered in the repot. The received estimation of PSF is used for the solution of task (compensation of PSF distortions) super-resolution.

Ultraresolution of microwave, color, and synthetic color images

The modern digital image forming systems are multi sensors or multi rays as a rule. The Modulation Transfer Function (MTF) MO of a Point Spread Function (PSF) O can be measured with the aid of special transparent image. PSF O of passive radio vision system can be measured for a point source. If Y is the ortho-normal system of Fourier harmonics in a small domain, then PSF O and MTF MO are connected by the eigen-values problem relative convolution and multiplication operations: O*Y=MO Y. We may introduce MTF MR of resolving function R: R*Y=MR Y and MTF MRO of (R*O): R*O*Y= MRO Y. We have [1] equality: MRO = MR MO in the frequency small domain. Ultra-resolution method gives point results of resolution and it is the most effective and stable method in order to increase resolution at present time. Examples of PSFs O, MTFs: MO, MR and MRO, and numerous applications of the ultra-resolution method are considered.

Superresolution in a multiray vision system with relative correction of rays

At Faculty of Physics, Moscow State University, the new super-resolution methods for different physical measuring systems are created. Special super-resolution methods for actual multi-rays systems of a millimeter wave range were developed. Until recent time the data obtained from an actual one-ray radio-vision system, were represented in such aspect: as though they were obtained from a virtual multi-rays system. Such an approach appears to be very successful: the problem of super-resolution has been solved at low values of a signal/noise ratio with the paralleled solutions on all the virtual rays. The paper is devoted to the problem of super-resolution of the data from actual compact 6-rays system of radio-vision. The experimental device of a 6-rays radio vision system was created without the mathematical modeling of its operation. It is possible even to tell that at the output of this system the poor results were gained. Therefore there was a problem to improve considerably the poor results: to increase the resolution of each ray. We suppose that obtained experience to be useful while constructing the modern all-weather multi rays real-time radio-vision systems. The methods of super-resolution of actual multi-rays microwave vision system is considered in the paper.

Applications of the local-linear method of super-resolution

The local-linear method of super-resolution was developed for the solution of problems of compensation (resolving) of PSF distortions at low values of a signal/noise ratio. The resolving function, noise factor and value of increased resolution are introduced into consideration. The mathematical questions of applications of the local-linear method of super-resolution and problem of parallel calculations are considered.

Comparative analysis of methods of superresolution

The concepts Point Spread Function (PSF) and Modulation Transfer Function (MTF) are base din the linear and local- linear methods of super-resolution. The resolving function, noise factor and value of achieved resolution are introduced into consideration. It is possible to make the definitions RPSF and RMTF for the resolved images. Values of the achieved resolutions will be estimated by the ratio of integral from RMTF to integral from MTF. It is possible to make the definitions NPSF and NMTF for the nonlinear iterative methods and similarly to estimate values of the achieved resolution. The report is devoted to the comparative analysis of the methods of super-resolutions.

Additional enhancement of resolution in multiray radio vision systems

The designers of modern devices of vision prefer a scanning step of receiving system antenna with a smaller size aperture than the main lobe pattern of the Point Spread Function. This report is devoted to the development and application of a local-linear method of additional resolution enhancement for such a receiving system in radio vision and optics.